solve this probability :a box contains 10 marble, seven of which are black and three are red.three marbles are drawn,one after the other without replacement. find the probability of choosing 1 red,1 black and 1 red marble. in that order
prob(red, black, red)
= (3/10)(7/9)(2/8)
= 7/120
3/10*7/9*2/8=7/120
A box contain 10 marbles 7 of which are Black and 3 are red. 3 marbles are drawn one after the other without replacement. Find the probability of choosing.A,one red one Black and one red in this other. B, two black marble.C,at least two black marbles. A, at most two black marbles.
What is the answer of the questions below
a box contains 10 marble, seven of which are black and three are red.three marbles are drawn, one after the other without replacement. find the probability of choosing i. two black marbles
ii. at least two black marbles
iii. at most two black marbles.
note; please your explanation should be a detailed one
To find the probability of choosing 1 red, 1 black, and 1 red marble in that order, we can break down the problem into three steps:
Step 1: Calculate the probability of selecting the first red marble.
Step 2: Calculate the probability of selecting the second black marble after selecting the first marble.
Step 3: Calculate the probability of selecting the third red marble after selecting the first two marbles.
Let's calculate each step:
Step 1: Probability of selecting the first red marble.
We have a total of 10 marbles, with 3 red ones. So, the probability of selecting a red marble first is 3/10.
Step 2: Probability of selecting the second black marble after selecting the first marble.
After selecting the first marble, there are 9 marbles remaining in the box, with 7 being black. So, the probability of selecting a black marble second is 7/9.
Step 3: Probability of selecting the third red marble after selecting the first two marbles.
After selecting the first two marbles, we are left with 8 marbles, with 2 being red. So, the probability of selecting a red marble third is 2/8.
To find the overall probability, we multiply the probabilities of each step together:
Probability = (3/10) * (7/9) * (2/8)
Simplifying the expression, we get:
Probability = (3/10) * (7/9) * (1/4)
Probability = 3/60
Therefore, the probability of choosing 1 red, 1 black, and 1 red marble in that order is 1/20, which is approximately 0.05 or 5%.