Mr. and Mrs. Smith each bought 10 raffle tickets. Each of their three children bought four tickets. If
4280 tickets were sold in all, what is the probability that the grand prize winner is:
a. Mr. or Mrs. Smith? b. one of the 5 Smiths? c. none of the Smiths?
a) The probability for one or the other is 10/4280 (1/428). For one of the two, add each of their probabilities (1/428)+(1/428) gives an answer of 1/214.
b) The probability for any one child is 4/4280 (1/1070). Adding together the three children's probability (1/1070)+(1/1070)+(1/1070) gives an answer of 3/1070.
c)Since the total tickets for the Smiths are 32 tickets, 4280-32 (4248) tickets are possessed by others. 4248/4280 (531/535) is the probability another will win.
a. 10/4280
0.0023
b. (10+12) = total tickets
22/4280 = 0.051
c. (4280-22) divided by 4280
0.9949
To find the probability, we need to determine the total number of tickets sold and the number of tickets held by the Smiths.
a. To find the probability that the grand prize winner is Mr. or Mrs. Smith, we need to calculate the number of tickets they have and divide it by the total number of tickets sold.
Mr. and Mrs. Smith each bought 10 tickets, so they have a total of 10 + 10 = 20 tickets.
The probability that the grand prize winner is Mr. or Mrs. Smith is given by:
Probability = Number of tickets held by Mr. or Mrs. Smith / Total number of tickets sold
Probability = 20 / 4280
b. To find the probability that the grand prize winner is one of the 5 Smiths, we need to calculate the total number of tickets held by the Smith family and divide it by the total number of tickets sold.
Mr. and Mrs. Smith each bought 10 tickets, so they have a total of 10 + 10 = 20 tickets.
Their three children bought 4 tickets each, so they have a total of 3 * 4 = 12 tickets.
The total number of tickets held by the Smiths is 20 + 12 = 32.
The probability that the grand prize winner is one of the 5 Smiths is given by:
Probability = Number of tickets held by the Smiths / Total number of tickets sold
Probability = 32 / 4280
c. To find the probability that none of the Smiths win, we need to subtract the probability of the Smiths winning from 1.
Probability = 1 - Probability of the Smiths winning
Probability = 1 - (Number of tickets held by the Smiths / Total number of tickets sold)
Let's calculate the probabilities.
a. Probability that the grand prize winner is Mr. or Mrs. Smith:
Probability = 20 / 4280
b. Probability that the grand prize winner is one of the 5 Smiths:
Probability = 32 / 4280
c. Probability that none of the Smiths win:
Probability = 1 - (32 / 4280)
To solve this problem, we need to determine the total number of tickets sold for each group and then calculate the probability based on those numbers.
a. Probability that the grand prize winner is Mr. or Mrs. Smith:
Both Mr. and Mrs. Smith bought 10 tickets each, so the total number of tickets they bought together is 10 + 10 = 20. To find the probability, we divide the number of tickets bought by Mr. or Mrs. Smith by the total number of tickets sold.
Probability = (Number of tickets bought by Mr. or Mrs. Smith) / (Total number of tickets sold)
Probability = 20 / 4280
b. Probability that the grand prize winner is one of the 5 Smiths:
In this case, we consider both Mr. and Mrs. Smith along with their three children. So the total number of Smiths is 5 (2 parents and 3 children), and each one of them bought 4 tickets. Therefore, the total number of tickets bought by the Smiths is 5 * 4 = 20. We divide this number by the total number of tickets sold to find the probability.
Probability = (Number of tickets bought by the Smiths) / (Total number of tickets sold)
Probability = 20 / 4280
c. Probability that the grand prize winner is none of the Smiths:
To find this probability, we need to subtract the probability of the grand prize winner being one of the Smiths from 1 (since the remaining probability would be none of the Smiths).
Probability = 1 - (Probability of winning by one of the Smiths)
Now, you can calculate the probabilities by substituting the respective numbers into the formulas above.