Hi, I am just doing some maths revision in light of my maths GCSE resit, which is very soon. I am sitting the higher paper for the first time, so some of the questions towards the end of the paper are very testing of my knowledge.
At the moment I am going over past papers and I have come stuck on a question. After looking through my books, I am yet to understand what the question is asking. if anyone could help me I would be eternally grateful!
Question:
Ten different names are put into a computer. One of the names is Jaspal.
a) On Monday, the computer chooses two names at random. the computer is set so that the same name CAN be chosen twice.
Show the probability that Jaspal is chosen at least once is 19/100.
(3 marks)
b)On Tuesday, the computer chooses two names at random. The computer is set so the name CANNOT be chosen twice.
Work out the probability that Jaspal is chosen now.
(3 marks)
Any help would be really appreciated! Thank you
Kind regards
Sam.
a) It's 1-probability of not choosing Jaspal
= 1 - (9/10)^2 = (100-81)/100 =
19/100
Sure, I'd be happy to help you with these probability questions.
a) On Monday, the computer chooses two names at random, and the same name can be chosen twice. We need to find the probability that Jaspal is chosen at least once.
To find this probability, we can first find the probability that Jaspal is not chosen at all and subtract it from 1.
The total number of possible outcomes is the number of ways to choose 2 names out of the 10 names, which can be calculated using the combination formula, denoted as "nCr." So, the total number of outcomes is:
Total outcomes = 10C2 = 10! / (2! * (10-2)!) = 45
The number of outcomes where Jaspal is not chosen at all is the number of ways to choose 2 names out of the remaining 9 names:
Outcomes without Jaspal = 9C2 = 9! / (2! * (9-2)!) = 36
So, the probability that Jaspal is not chosen at all is 36/45.
Now, to find the probability that Jaspal is chosen at least once, we subtract the probability of not choosing Jaspal from 1:
Probability of choosing Jaspal at least once = 1 - 36/45 = 9/45 = 1/5 = 19/100
Therefore, the probability that Jaspal is chosen at least once on Monday is 19/100.
b) On Tuesday, the computer chooses two names at random, but the same name cannot be chosen twice.
The total number of possible outcomes is the number of ways to choose 2 names out of the 10 names, which is 10C2 = 45, as calculated earlier.
The number of outcomes where Jaspal is chosen is the number of ways to choose Jaspal as one of the names and any other name for the second choice, which is 1 * 9 = 9.
So, the probability that Jaspal is chosen on Tuesday is 9/45, which simplifies to 1/5.
Therefore, the probability that Jaspal is chosen on Tuesday is 1/5 or 20/100.
I hope this helps you understand the questions and how to calculate the probabilities. Good luck with your maths revision and your GCSE resit! Let me know if you have any further questions.
Hi Sam! I can definitely help you with these probability questions.
Let's tackle part (a) first. The question states that there are ten different names in the computer and one of them is Jaspal. On Monday, the computer chooses two names at random, and it is possible for the same name to be chosen twice.
To find the probability that Jaspal is chosen at least once, we need to calculate the probability of Jaspal being chosen once and the probability of Jaspal being chosen twice, and then add them together.
Probability of Jaspal being chosen once:
Since there are ten different names, the total number of possible pairs of names is given by the combination formula: C(10,2) = 10! / (2!(10-2)!), which simplifies to 45.
Out of these 45 pairs, we want to find the ones that include Jaspal. Jaspal can be chosen for the first spot in the pair, or for the second spot, so there are two possibilities.
Therefore, the probability of Jaspal being chosen once is 2/45.
Probability of Jaspal being chosen twice:
There is only one possibility for Jaspal being chosen twice, since there is only one Jaspal and the same name can be chosen twice. So the probability is 1/45.
Now, to find the probability that Jaspal is chosen at least once, we add the probabilities together:
2/45 + 1/45 = 3/45 = 1/15.
Therefore, the probability that Jaspal is chosen at least once on Monday is 1/15 or 19/100 (as given in the question).
Moving on to part (b), on Tuesday, the computer still chooses two names at random, but now the same name cannot be chosen twice.
To find the probability of Jaspal being chosen, we need to consider two cases:
Case 1: Jaspal is chosen both times
Case 2: Jaspal is chosen once out of the two times
Case 1:
Since Jaspal cannot be chosen twice, the probability of Jaspal being chosen both times is zero.
Case 2:
The probability of Jaspal being chosen once out of the two times can be calculated similar to part (a).
The total number of pairs of names is again given by C(10,2) = 45.
Out of these 45 pairs, Jaspal can be chosen for the first spot in the pair, or for the second spot, so there are two possibilities.
Therefore, the probability of Jaspal being chosen once is 2/45.
Since Case 1 has a probability of zero, we only need to consider Case 2.
Therefore, the probability that Jaspal is chosen on Tuesday is 2/45.
I hope this explanation helps you understand the questions better and how to calculate the probabilities. If you have any further questions, feel free to ask! Good luck with your maths GCSE resit!