Five people each fip a coln one time. Find each theoretical probability. 19. P(e

Question

Five people each fip a coln one time. Find each theoretical probability. 19. P(exactly 2 tails) 18. P(5 heads) 20. P(at least 3 heads) 22. The spinner shown at the right has four equal-sized sections. Suppose 21. P(less than 4 tails) you spin the spinner two times. a. What is the sample space? b. How many outcomes are there? c. What is the theoretical probability of getting a sum of 4? 23. Ifx is a real number and x - o, what is the probability that is undefined? 24. If x is a real number and x # 0, what is the probability that is undefined? 25. Of the 195 students in the senior class, 104 study Spanish and 86 study with 12 studying both Spanish and French. What is the theoretical proba that a student chosen at random is studying Spanish, but not Frend biliry

Explanation / Answer

P(head) = 1/2

P(tail) = 1/2

a)

P(5 heads) = (1/2)5

b)

exactly 2 tails means 2 tails and 3 heads

P(exactly 2 tails) =5C2 * P(2 tails and 3 heads)

= 10* {P(tail)}2*{P(head)}3  

=10* (1/2)2*(1/2)3

=10*(1/2)5

c)

P(at least 3 heads) =5C3* P(exactly 3 heads) +5C4* P(exactly 4 heads) + P(exactly 5 heads)

=10*P(exactly 3 heads and 2 tails)+5*P(exactly 4 heads and 1 tail) + P(exactly 5 heads)

=10*(1/2)3(1/2)2 + 5*(1/2)4(1/2) + (1/2)5

= 16*(1/2)5 = 1/2

d)

P(less than 4 tails) = P(no tails) + 5C1* P(exactly 1 tail) +5C2* P(exactly 2 tails) + 5C3* P(exactly 3 tails)

=P(exactly 5 heads) + 5*P(exactly 4 heads and 1 tail) + 10*P(exactly 3 heads and 2 tails) + 10 *P(exactly 2 heads and 3 tails)

=26*(1/2)5

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