1) What is the probability of tossing 6 coins and getting at least two tails?

Question

2) Suppose you flip a penny, a nickel,a dime and a quarter. What is the probability of getting heads on the penny and nickel and dime and tails on the quarter?

Please show steps for the solutions.
Thank you.

Answer 1

p tails in 1 toss = .5
binomial distribution
p = .5
number of trials , n , = 6
number of successes = 2,3,4,5,6
number of failures = 0,1
so easier to work it backwards
what is the probability of 0 or 1 heads
p is still .5
p(0 heads) = C(6,0) (.5^0)(.5)^6 = .0156
p(1 heads) = C(6,1)(.5^1)(.5)^5 = 3*.03125 = .09375
sum = about .11
1 - .11 = .89

Answer 2

Suppose you flip a penny, a nickel,a dime and a quarter. What is the probability of getting heads on the penny and nickel and dime and tails on the quarter?
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independent experiments
1/2*1/2*1/2*1/2

Answer 3

a dime rolled 5 times find the probability of getting 4 exactly 5 times