There are 5 red and 9 green balls in a bag. If you randomly choose balls one at a time, with replacement, what is the probabilit
2 answers:
Answer:
The probability of choosing 2 red balls and then 1 green ball is:
225/2744
Step-by-step explanation:
There are 5 red and 9 green balls in a bag.
Total balls=5+9=14
We randomly choose balls one at a time, with replacement.
(we draw a ball, look at it and place it in the bag and then draw another one)
P(choosing 2 red balls and then 1 green ball)
=
= 225/2744
Hence, the probability of choosing 2 red balls and then 1 green ball is:
225/2744
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In the Triangle ABD, Using Pythagoras theorem we can write
In the Triangle ACD using Pythagoras Theorem
Now in the larger Triangle ABC, we can write
Now substitute the values from the above equations we get
Answer:
d. 0.303
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
In this question:
We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.
Distribution of the difference between Sean's and Evan's income:
Sean has mean 225, Evan 240. So
Sean's standard deviation is of 25, Evan's of 15. So
Probability that Sean will have a greater income than Evan in a randomly selected week:
Probability of the subtraction being greater than 0, which is 1 subtracted by the pvalue of Z when X = 0. So
has a pvalue of 0.695
1 - 0.695 = 0.305.
Closest to 0.303, option d.