Cecile tosses 5 coins,one after the other.
a) How many different outcomes are possible?
b) In how many ways will the first coin turn up heads and the last coin turn up tails?
c) In how many ways will the second third and fourth coins all turn up heads?
d) would the same possibilities arise in parts a) b) and c) if one coin was tossed 5 times in succession?
and just to understand the question what would a tress diagram look like illustrating the possibilities.
Did you ever find the answer to this qustion?... i'm doing the exact same course and need help with it!
To answer these questions, let's break them down step by step:
a) How many different outcomes are possible?
To find the number of different outcomes when tossing multiple coins, we can multiply the number of possibilities for each individual coin toss. Since each coin has two possible outcomes (heads or tails), and Cecile tosses 5 coins, the total number of different outcomes is 2 x 2 x 2 x 2 x 2 = 32.
b) In how many ways will the first coin turn up heads and the last coin turn up tails?
To calculate the number of ways the first coin can turn up heads (1 possibility) and the last coin can turn up tails (1 possibility), we multiply the number of possibilities for each event. So, there is 1 x 2 x 2 x 2 x 1 = 8 ways for the specified outcome to occur.
c) In how many ways will the second, third, and fourth coins all turn up heads?
Similarly, there is 2 x 1 x 1 x 1 x 2 = 4 ways for the second, third, and fourth coins to all turn up heads. This is because the first and fifth coins can have any outcome (2 possibilities each), while the middle three coins must all be heads (1 possibility each).
d) Would the same possibilities arise in parts a), b), and c) if one coin was tossed 5 times in succession?
If one coin was tossed 5 times in succession, the total number of outcomes in part a) would remain the same since each toss still has 2 possibilities. However, the specific outcomes in parts b) and c) would change because the position of the coins matters. In the case of tossing one coin 5 times, there would only be one way for the first coin to be heads and the last coin to be tails (HHHHT), and similarly, only one way for the second, third, and fourth coins to all be heads (HHHHH).
As for the tree diagram, it would look like this:
H T
/ \
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
Each level represents a toss, and the branches represent the possible outcomes (H for heads, T for tails).
I hope this helps! Let me know if you have any further questions.