Mark H. answered • 12/18/20
Experienced Tutor Specializing in Algebra, Geometry, and Calculus
A bag contains 3 blue marbles, 10 yellow marbles, 5black marbles. If one marble is drawn from the bag then replaced, what is the probability of drawing a blueblue marble then a blackblack marble?
Need to find P(blue and black) = P(blue)*P(black) **(since events are independent).
P(blue on 1st draw) = 3/(3+10+5) = 3/18
P(black on 2nd draw with replacement) = 5/(3+10+5 ) = 5/18.
Therefore, P(blue)*P(black) = (3/18)*(5/18) = 15/(182) = 15/324
In a number guessing game. You ask a person to guess a number from one 1 to 10. If the person makes a random guess, what is the probability their guess will be less than 9?
Let X be an event where a random number is chosen from 1 to 10.
Then P( X < 9) = 1 - P( X>= 9) = 1 - (P(X = 9 or X =10)) = 1 - (1/10 + 1/10) = 1 - 2/10 = 8/10.
**Note: P(X < 9) + P (X >= 9) = P(1) + P(2) +...+ P(10) = 10*(1/10) = 1
There are 8 slots to choose from with success (number is less than 9) and 2 slots to choose from with failure (number is greater than or equal to 9).
A bag contains 10white marbles, 5black marbles, 3yellow marbles. If one marble is drawn from the bag but not replaced, what is the probability of drawing a white marble then a yellow marble?
This is the same case as question 1, except the ball is NOT replaced. Therefore, the total number of marbles on 2nd draw changes from 18 (initial amount) to 18-1 = 17.
P(white)*P(yellow) = P(white)*P(yellow) = 10/(10 + 5 + 3) * 3/(10 + 5 + 3 - 1) = 10/18*3/17 = 30/306
