Suppose that 61% of students in a college have a smart phone. If you select three students at random, what is the probability that all three have a smart phone?
Give your answer as a decimal (to at least 3 places) or fraction
Well, let me calculate that for you. Since each student has a 61% chance of having a smart phone, the probability that the first student has a smart phone is 0.61. Now, when selecting the second student at random, the probability that they have a smart phone is also 0.61. Finally, when choosing the third student, the probability is once again 0.61. To find the probability of all three students having a smart phone, we multiply these probabilities together: 0.61 * 0.61 * 0.61 = 0.226. So, the probability is approximately 0.226, or if you prefer a fraction, it would be about 113/500.
To find the probability that all three selected students have a smart phone, we need to multiply the individual probabilities of each student having a smart phone.
Given that 61% of students in the college have a smart phone, the probability of a single student having a smart phone is 61% or 0.61.
Since we are selecting three students at random, we assume that the selections are independent events. This means that the probability of the first student having a smart phone does not affect the probability of the second and third students having a smart phone.
Thus, to find the probability that all three students have a smart phone, we multiply the probability of the first student having a smart phone by the probability of the second student having a smart phone, and then multiply that by the probability of the third student having a smart phone:
P(all three students have a smart phone) = 0.61 * 0.61 * 0.61 = 0.2261.
Therefore, the probability that all three selected students have a smart phone is 0.2261 or approximately 0.226 (to three decimal places).
To find the probability that all three students have a smartphone, we need to multiply the probabilities of each event happening.
The probability of the first student having a smartphone is 61% or 0.61, since 61% of students have a smartphone.
The probability of the second student having a smartphone is also 0.61, since each student is selected independently.
Similarly, the probability of the third student having a smartphone is also 0.61.
To find the probability of all three events happening, we multiply the probabilities together:
P(all three have a smartphone) = P(first has a smartphone) * P(second has a smartphone) * P(third has a smartphone)
P(all three have a smartphone) = 0.61 * 0.61 * 0.61
Calculating this, we get:
P(all three have a smartphone) = 0.226
So, the probability that all three students have a smartphone is approximately 0.226 or 22.6%.