Makalo has five cards, numbered 1 to 5. He picks one card at random, replaces that card back in with the others, and then picks a second card.
The tree diagram below shows the probability of Makalo getting an even or an odd number with each pick.
1st pick
Even - 0.4
Even - 0.4
2nd pick
Odd - 0.6
Odd - 0.6
Even - 0.4
Odd - 0.6
Use the tree diagram to find the probability that Makalo:
a) gets an odd number with both picks
b) gets an even number with both picks
c) gets an odd number on the first pick and an even number on the second
d) an odd number and an even number, in either order
a) To find the probability that Makalo gets an odd number with both picks, we multiply the probabilities along the branches that lead to an odd number on both picks:
0.6 * 0.6 = 0.36
So, the probability that Makalo gets an odd number with both picks is 0.36.
b) To find the probability that Makalo gets an even number with both picks, we multiply the probabilities along the branches that lead to an even number on both picks:
0.4 * 0.4 = 0.16
So, the probability that Makalo gets an even number with both picks is 0.16.
c) To find the probability that Makalo gets an odd number on the first pick and an even number on the second, we multiply the probabilities along the branches that lead to an odd number on the first pick and an even number on the second:
0.6 * 0.4 = 0.24
So, the probability that Makalo gets an odd number on the first pick and an even number on the second is 0.24.
d) To find the probability that Makalo gets an odd number and an even number, in either order, we need to calculate the sum of the probabilities from parts a) and c):
0.36 + 0.24 = 0.6
So, the probability that Makalo gets an odd number and an even number, in either order, is 0.6.
To find the probability for each event, we can follow the branches of the tree diagram and multiply the probabilities along the way. Let's calculate the probabilities for each event:
a) Getting an odd number with both picks:
The probability of getting an odd number in the first pick is 0.6, and the probability of getting an odd number in the second pick, given an odd number in the first pick, is also 0.6.
Probability of getting an odd number with both picks = 0.6 * 0.6 = 0.36
Therefore, the probability that Makalo gets an odd number with both picks is 0.36.
b) Getting an even number with both picks:
The probability of getting an even number in the first pick is 0.4, and the probability of getting an even number in the second pick, given an even number in the first pick, is also 0.4.
Probability of getting an even number with both picks = 0.4 * 0.4 = 0.16
Therefore, the probability that Makalo gets an even number with both picks is 0.16.
c) Getting an odd number on the first pick and an even number on the second:
The probability of getting an odd number in the first pick is 0.6, and the probability of getting an even number in the second pick, given an odd number in the first pick, is 0.4.
Probability of getting an odd number on the first pick and an even number on the second = 0.6 * 0.4 = 0.24
Therefore, the probability that Makalo gets an odd number on the first pick and an even number on the second is 0.24.
d) Getting an odd number and an even number, in either order:
We can calculate this probability by summing the probabilities from events a) and c).
Probability of getting an odd number and an even number, in either order = Probability of getting an odd number with both picks + Probability of getting an odd number on the first pick and an even number on the second
= 0.36 + 0.24 = 0.60
Therefore, the probability that Makalo gets an odd number and an even number, in either order, is 0.60.
Please let me know if anything is unclear or if there is anything else I can help you with!