1.Four coins are tossed.What is the probability of tossing all heads?
2.A card is chosen at random from a deck of 52 cards.It is then replaced and a second card is chosen.What is the probability of getting a jack and then an eight?
1/169
To find the probability of tossing all heads in a situation where four coins are tossed, we need to determine the total number of possible outcomes and the number of favorable outcomes.
1. Total number of outcomes:
When flipping a coin, there are two possible outcomes for each flip - heads or tails. Since there are four coins being tossed, the total number of outcomes can be calculated as 2^4 = 16 (as each coin flip is independent).
2. Number of favorable outcomes:
To obtain all heads, we need to get heads on each of the four coins. This can only happen in one way - H-H-H-H.
Therefore, the number of favorable outcomes is 1.
3. Probability calculation:
The probability is obtained by the ratio of favorable outcomes to total outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
Probability of tossing all heads = 1/16 or 0.0625 (6.25%)
Now let's move on to the second question:
To find the probability of getting a jack and then an eight when selecting two cards from a standard deck of 52 cards (with replacement):
1. Total number of outcomes:
When selecting a card from the deck, there are 52 possible outcomes (as each card has an equal chance of being chosen). Since there are two card selections, we multiply the possibilities, giving us 52 * 52 = 2,704 total outcomes.
2. Number of favorable outcomes:
To obtain a jack and then an eight, we need to consider that getting a jack and an eight can only happen in one particular order. There are 4 jacks and 4 eights available in the deck. The favorable outcome is J-8.
So, the number of favorable outcomes is 4 * 4 = 16.
3. Probability calculation:
The probability is obtained by the ratio of favorable outcomes to total outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
Probability of getting a jack and then an eight = 16/2704 or 0.00592 (0.592%)
By following the steps mentioned above, we can calculate the probabilities for both questions.