Question 6) a) You toss a fair coin 2 times. What is the chance that you will ge

Question

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?

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

Explanation / Answer

a)

If coin is tossed 2 times, so the outcome are { HH, HT, TH,TT}

so the chances or probability of both heads is =1/4.

b)

If a coin is tossed 4 times, so the outcome are 2^4=16

The chances or probability of all the outcomes are heads is 1/16.

c)

If a coin is tossed 10 times, so the outcome are 2^10= 1024

The chances or probability of all the outcomes are heads is 1/1024.

d)

If a coin is tossed 21 times, so the outcome are 2^21= 2097152

The chances or probability of all the outcomes are heads is 1/2097152.

e)

In 1 min= 20 times coin tossed

60 min = 1200 times

1 day = 28800 times

so it will complete 2097152 times in = 2097152/28800= 72.81 days.

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