Gina has a spinner with five equal parts numbered one thru five. If Gina spins the spinner one time, what is the probability tha
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Answer:
a) 0.0156 = 1.56% probability that all children will develop the disease.
b) 0.4219 = 42.19% probability that only one child will develop the disease.
c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The probability that their offspring will develop the disease is approximately .25.
This means that
Three children:
This means that
Question a:
This is P(X = 3). So
0.0156 = 1.56% probability that all children will develop the disease.
Question b:
This is P(X = 1). So
0.4219 = 42.19% probability that only one child will develop the disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Third independent of the first two, so just multiply the probabilities.
First two do not develop, each with 0.75 probability.
Third develops, which 0.25 probability. So
0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
Answer:
The probability that the card selected bears a number less than 34 is 0.3333.
Step-by-step explanation:
Let random variable <em>X</em> be defined as the number on the selected card.
There are <em>N</em> = 15 total cards.
The number on the cards are as follows:
S = {25, 26, 27,..., 38, 39}
The probability of an event, <em>E</em> is the ratio of the number of favorable outcomes to the total number of outcomes.
In this case we need to compute the probability that the card selected bears a number less than 34.
The favorable outcomes are:
<em>s</em> = {25, 36, 37, 38, 39}
<em>n</em> (X < 34) = 5
Compute the probability that the card selected bears a number less than 34 as follows:
Thus, the probability that the card selected bears a number less than 34 is 0.3333.