Select Two Cards In a board game uses the deck of 20 cards shown. first roll has five birds 2 yellow, 3 red, second roll 5 lions same, third roll five frogs the same, fourth roll has five monkeys the same. Two cards are selected at random from this deck. Determine the probability of the following, a)with replacement. b)without replacement. They both show even numbers.
You don't show any deck of 20 cards.
It is not clear what is being "rolled". You said these were cards, not dice.
You never mentioned the cards showing numbers, only animals.
I am completely confused by your queastion.
To determine the probability of selecting two cards, we need to know how many cards in the deck satisfy the given condition (show even numbers). Let's calculate this.
In the deck of 20 cards, we have:
- 5 yellow birds (odd numbers)
- 3 red birds (odd numbers)
- 5 lions (even numbers)
- 5 frogs (odd numbers)
- 2 monkeys (even numbers)
a) With Replacement:
When selecting with replacement, it means that after selecting a card, it is placed back into the deck before the next selection. Thus, the number of favorable outcomes remains the same for each selection.
To find the probability of both selected cards showing an even number with replacement, we need to determine the probability of selecting an even number on each turn.
First roll: There are 20 cards in total, and 7 of them are even numbers (5 lions + 2 monkeys). Therefore, the probability of selecting an even number on the first roll is 7/20.
Second roll: Since the first card is replaced, we still have 20 cards in the deck. The number of even numbers remains the same at 7. So the probability of selecting an even number on the second roll is also 7/20.
To find the probability of both events occurring, we multiply the probabilities together:
Probability (with replacement) = (7/20) * (7/20) = 49/400 ≈ 0.1225
b) Without replacement:
When selecting without replacement, it means that after selecting a card, it is not placed back into the deck before the next selection. Therefore, the probability of the second card depends on what was selected first.
To find the probability of selecting two cards from the deck without replacement, showing even numbers, we calculate it step by step:
First roll: There are 20 cards in the deck, and 7 of them are even numbers. Therefore, the probability of selecting an even number on the first roll is 7/20.
Second roll: After removing one card from the deck, we have 19 cards left. If the first card selected was even, there are now 6 even numbers left out of 19 cards. If the first roll results in an odd number, there are still 7 even numbers left out of 19 cards. Thus, the probability of selecting an even number on the second roll depends on the first roll's outcome.
To find the overall probability, we consider the two possible scenarios and weigh them according to their probabilities:
Probability (without replacement) = [(7/20) * (6/19)] + [(13/20) * (7/19)]
= 42/380 + 91/380
= 133/380 ≈ 0.350
Therefore, the probability of selecting two cards, both showing even numbers, is approximately 0.1225 with replacement, and approximately 0.350 without replacement.