This problem consists of 5 different probabillity questions You toss a coin 4 ti

Question

This problem consists of 5 different probabillity questions You toss a coin 4 times. How many possible results does the sample space contain? You spin a roulette wheel that has 11 slots twice. How many possible results does the sample space contain? You roll two dice. What is the chance that both will show the same number (eg two 6's)? You roll two dice. What is the chance that the total will be greater than 7? You toss a coin 3 times,. Given that the first toss is tails, what is the chance that you get exactly 2 tails out of the 3 tosses?

Explanation / Answer

1. A coin is tossed 4 times.

A coin has 2 faces, so possible results in sample space = 2*2*2*2 = 2^4 = 16 ways

2. Possible results of Roulette' wheel sample space is = 11C2 = 11*10/2 = 55 ways

3.2 die are rolled. Chances that same number comes up in both = ?

Choose 1 number in 1st die in 6C1 ways. After choosing this number you can choose this number on 2nd number in 1 way. Chances that same number comes up in both = 6C1*1/6C1*6C1 = 1/6 are the chances

4. P(total is greater than 7) = P(total is 8,9,10,11,12) = ?

P(sum = 8) = (4,4),(5,3),(3.5),(6,2),(2,6) = 5 ways

P(sum = 9) = (6,3),(3,6), (5,4),(4,5), = 4 ways

P(sum=10) = (6,4),(4,6),(5,5) = 3 ways

P(sum=11) = (6,5),(5,6) = 3 ways

P(sum=12) = 6,6 = 1 ways

P(sum=12) = (6,6)= 1 way

P(total is greater than 7) = P(total is 8,9,10,11,12) = 16/36 = 4/9

5. THH, THT, TTH, TTT are possible elements in sample space with 1st as tails.

P( 2 tails out of 3 tosses) = THT, TTH out of 4 above cases = 2/4 = 1/2

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