Question 5) In a lotto game, exactly five balls are selected from an urn contain

Question

Question 5) In a lotto game, exactly five balls are selected from an urn containing balls numbered from 1 to 50.

a) If your ticket contains a list of 5 distinct numbers, what is the chance that you will win the lottery (that is, the numbers drawn will be exactly the same as in your bet)?

b) What is the chance that your ticket will have 4 out of the 5 selected numbers?

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Question 6)

a) You toss a fair coin 2 times. What is the chance that you will get a sequence of 2 heads?

b) You toss a fair coin 4 times. What is the chance that you will get that in each and every time the outcome is heads?

c) You toss a fair coin 10 times. What is the chance that all the outcomes are heads?

d) You toss a fair coin 21 times. What is the chance that all the outcomes will be heads? Compare it to the chance you found on part (a) of question 5.

e) Small numbers are sometimes hard to make sense of. To put them into perspective, think about the following: If takes you one minute to toss the coin 20 times, and this is the only thing you do every day and night until you toss it 2.097.152 times (which is equal to 2^21), how long would it take you to complete your task? Compare that number to how old you are.

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I am struggling with this stat homework. Please help! Thank you :)

Explanation / Answer

(5) n(S) = 50 * 49 * 48 * 47 * 46 = 254251200

(a) n(All 5 numbers match) = 1

Probability = 1/254251200

(b) n(One number does not match) = 5 * 45 = 225

Probability = 225/254251200

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