4. A piata is a container filled with toys and candy and is broken open by...
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4. A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. The drawing above shows Sophia trying to break a piñata. The probability that she will break the pifiata on the first hit is 0.7. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break it on the next hit is 0.1 greater than the probability on the previous hit. For example, if the pifiata does not break on the first hit, the probability that it will break on the second hit is 0.8. (a) Calculate the probability that Sophia does not break the pifiata on the first hit and does break the piñata on the second hit. Let the random variable X represent the number of hits required for Sophia to break the piñata. (b) Complete the probability distribution of X in the table below. 2 3 4 Probability of x 0.7 4. A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. The drawing above shows Sophia trying to break a piñata. The probability that she will break the pifiata on the first hit is 0.7. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break it on the next hit is 0.1 greater than the probability on the previous hit. For example, if the pifiata does not break on the first hit, the probability that it will break on the second hit is 0.8. (a) Calculate the probability that Sophia does not break the pifiata on the first hit and does break the piñata on the second hit. Let the random variable X represent the number of hits required for Sophia to break the piñata. (b) Complete the probability distribution of X in the table below. 2 3 4 Probability of x 0.7
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