Question

100 points

When Yehudi and Carlos play racquetball, the probability that Yehudi wins a point is 0.35.

a) How many points would you expect Yehudi to win from the first 15 points? Give your answer to the nearest whole number of points.

b) Choose the correct terms in the following statement.
If Yehudi won 10 out of the first 15 points I would [not be/ be slightly/ be very] surprised as the number is [about the same as/ just above/ well above] the expected number. ​

Answer 1

a) For every 1 point, Yehudi wins 0.35 points.

Thus, for
`15` points, Yehudi will win $15 \times 0.35= 5.25$ points.

b) You know what to do :)

Answer 2

When you repeat the same experiment over and over, and all experiments are independent, you are following a Bernoulli distribution. If you perform
`n` experiments, and you have probability of succeeding
`p` for each experiment, the expected number of successes is

`\mathbb{E}(X)=np`

In your case, you perform 15 experiments, with a probability of success of 0.35 per experiment. So, we expect

`np=15\cdot 0.35=5.25`

Since 10 is about twice the number of expected points, it would be very surprising.