In a game, a player tosses a coin 4 times. If the player gets 3 or 4 heads, he/she wins. What is the theoretical probability of winning this game?
I just need to know the outcomes. I don't know how to get them.
Please and Thank you.
Coin 1: 50% Heads
Coin 2: 50% Heads
Coin 3: 50% Heads
Coin 4: Irrelevent, because only 3 are needed.
50% x 50% x 50% = 12.5%
12.5%
When you want to know the probability of all events occurring, multiply the probability of the individual events.
When you want to know the probability of either one event or another occurring, add the individual probabilities.
Probability of 3 heads is 1/2*1/2*1/2. Since the probability of the remaining toss can be either heads or tails, its proability is 1/2+1/2=1, so this has no effect on the multiplication. Probability of 3 heads = 1/8
Probability of 4 heads is 1/2*1/2*1/2*1/2 = 1/16.
The probability of getting either 3 heads or 4 heads is found by adding the two probabilities.
1/8 + 1/16 = 2/16 + 1/16 = 3/16 = 18.75%
I hope this helps a little more. Thanks for asking.
To calculate the theoretical probability of winning the game, we need to consider the possible outcomes of tossing the coin 4 times.
Each coin toss has 2 possible outcomes: heads or tails. Since there are 4 coin tosses, the total number of possible outcomes is 2^4 = 16.
Now, let's determine the number of favorable outcomes, which in this case are the outcomes where the player gets 3 or 4 heads.
For getting 3 heads, there are 4 ways this can happen:
1. HHTT
2. HTHT
3. HTHH
4. THHH
For getting 4 heads, there is only 1 way this can happen:
1. HHHH
So, the number of favorable outcomes is 4 + 1 = 5.
Now, we can calculate the theoretical probability of winning the game by dividing the number of favorable outcomes by the total number of possible outcomes:
P(Winning) = Number of favorable outcomes / Total number of possible outcomes = 5 / 16 = 0.3125
Therefore, the theoretical probability of winning the game is 0.3125 or 31.25%.