a. Probability that the coin shows tails is [tex]\frac{1}{4}[/tex].
b. 50 number of times the coin shows tails.
What is probability?
Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
Probability = [tex]\frac{Number \ of \ favorable \ outcomes}{Total \ number \ of \ favorable \ outcomes}[/tex]
According to the question
a. John throws a biased coin 120 times. It shows heads 90 times.
Probability formula:
Probability = [tex]\frac{Number \ of \ favorable \ outcomes}{Total \ number \ of \ favorable \ outcomes}[/tex]
Probability that the coin shows heads = [tex]\frac{90}{120}[/tex] = [tex]\frac{3}{4}[/tex]
Probability that the coin shows tails = 1 - [tex]\frac{3}{4}[/tex] = [tex]\frac{1}{4}[/tex]
b. Carly throws the same coin 200 times.
From a, we know the probability that the coin shows tails is [tex]\frac{1}{4}[/tex].
Number of times the coin shows tails = 200 × [tex]\frac{1}{4}[/tex] = 50
Find out more information about probability here
brainly.com/question/13011617
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