Answered

Get expert insights and community-driven knowledge on IDNLearn.com. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.

7. Three different coins are tossed together. Find the probability of getting:

a) Exactly 2 heads
b) At least 2 heads
c) At most 2 tails

Sagot :

GinnyAnsweridn
Absolutely! Let's tackle this problem step by step.

### Total Possible Outcomes:
When tossing three coins, each coin has two possible outcomes: Heads (H) or Tails (T).
Thus, the total number of possible outcomes when three coins are tossed is:

[tex]\[ 2^3 = 8 \][/tex]

These possible outcomes are:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

### a) Probability of getting exactly 2 heads:

First, we need to list out the outcomes where exactly two heads appear:
- HHT
- HTH
- THH

There are 3 outcomes with exactly 2 heads.

The probability of getting exactly 2 heads is the number of favorable outcomes divided by the total number of possible outcomes:

[tex]\[ P(\text{exactly 2 heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{8} \][/tex]

So, the probability is:

[tex]\[ P(\text{exactly 2 heads}) = 0.375 \][/tex]

### b) Probability of getting at least 2 heads:

Next, we list out the outcomes where there are at least 2 heads. This includes all cases of exactly 2 heads and the case where there are 3 heads:
- HHT (2 heads)
- HTH (2 heads)
- THH (2 heads)
- HHH (3 heads)

There are 4 outcomes with at least 2 heads.

The probability of getting at least 2 heads is:

[tex]\[ P(\text{at least 2 heads}) = \frac{4}{8} \][/tex]

So, the probability is:

[tex]\[ P(\text{at least 2 heads}) = 0.5 \][/tex]

### c) Probability of getting at most 2 tails:

Finally, we count the outcomes where there are at most 2 tails. This includes all cases where there are 0, 1, or 2 tails:
- HHH (0 tails)
- HHT (1 tail)
- HTH (1 tail)
- THH (1 tail)
- HTT (2 tails)
- THT (2 tails)
- TTH (2 tails)

There are 7 outcomes with at most 2 tails.

The probability of getting at most 2 tails is:

[tex]\[ P(\text{at most 2 tails}) = \frac{7}{8} \][/tex]

So, the probability is:

[tex]\[ P(\text{at most 2 tails}) = 0.875 \][/tex]

### Summary of Results:

a) Probability of getting exactly 2 heads: [tex]\( \boxed{0.375} \)[/tex]

b) Probability of getting at least 2 heads: [tex]\( \boxed{0.5} \)[/tex]

c) Probability of getting at most 2 tails: [tex]\( \boxed{0.875} \)[/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.